Consider the vehicle data in Figure 11.30 from Consumer Reports. Weight is in tons, mileage in miles per gallon, and drive ratio is also indicated. A regression model was fitted relating weight x to mileage y. A partial SAS printout in Figure 11.30 shows some of the results of that regression analysis and Figure 11.31 gives plot of the residuals and weight for each vehicle.
Figure 11.30

(a) From the analysis and the residual plot, does it appear that an improved model might be found by using a transformation? Explain.
(b) Fit the model by replacing weight with log weight. Comment on the results,
(c) Fit a model by replacing mpg with gallons per 100 miles traveled, as mileage is often reported in other countries. Which of the three models is preferable? Explain.

Obs Model AG DR RATIO 16.9 1 Buick Estate Wagon 2 Ford Country Squire Wagon 4.360 Chery Ma libu Wagon 3.605 3.940 19.2 18.5 4 Chrysler LeBaron Wagon 5 Chevette 6 Toyota Corona 7 Datsun 510 2.560 2.300 27.5 27.2 Audi 5000 10 Volo 240 CL Saab 99 GLE 2.795 21.6 11Peuot 694 SL 13 Buick Century Special 14 Mercury Zephyr 3.070 3.620 20.8 18.6 Dodge Aspen 16 AAC Concord D/L 17 Chery Caprice Classie 18 Ford LTP 19Mercury Grand Marquis 3.72517.6 3.935 3.830 18.2 2.585 26.5 2.910 21.9 1.97 34.1 1.915 35.1 2.670 27.4 1.990 31.5 Dodge St Regis Ford Mustang 4 Ford Mustang Ghia Macda GLC 24 Dodge Colt AC Spirit 26 VW Scirocco 27 Honda Accord L 28Buick Skylark 29Chevy Citation 30 Olds Omega 31 Pontiac Phoenix 32 Plymouth Horizon 33 Datsun 210 2.570 28.4 2.595 28.8 2.700 26.8 2.020 31.8 Fiat Strada VW Dasher Datsun 810 BW 3201 2.190 30.5 2.815 22.0 36 W Rabbit Root SE 2.837580 APG Mean 24.76053 0.817244 11.46010 Standard Erro t Value Pr iti Paramster Intercept Estimate 48.67928080 -8.36243141 1.94053995 0.65908398 s.0001 .0001